Back to Prove system equivalence — Problem 3 · Task Set 40

Exercises: Prove That the Elimination Method Preserves Solution Sets

Work through each section in order. For proof problems, write complete logical arguments — state what you assume, what you conclude, and which properties justify each step.

Grade 9·19 problems·~40 min·Common Core Math - HS Algebra·standard·hsa-rei-c-5

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Fluency Practice

Prove Direction 1 of the REI.C.5 theorem: if $(x_0, y_0)$ is any solution of the original system ( $E_1 = 0$ and $E_2 = 0$ ), then $(x_0, y_0)$ also satisfies the new equation $E_1 + k \cdot E_2 = 0$ .

Write a complete proof with each step and its justification.